# A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

## TL;DR

This paper introduces a finite volume method tailored for elastoviscoplastic flows, incorporating stabilization techniques and applied to lid-driven cavity simulations to compare with traditional models.

## Contribution

It presents a novel finite volume approach with stabilization techniques for elastoviscoplastic flow simulation, extending existing viscoelastic methods to more complex materials.

## Key findings

- Successfully simulated lid-driven cavity flow with the new method.
- Compared elastoviscoplastic and Herschel-Bulkley models, showing differences in flow behavior.
- Analyzed flow cessation dynamics after stopping the lid.

## Abstract

We propose a Finite Volume Method for the simulation of elastoviscoplastic flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154-161]. The method is akin to methods for viscoelastic flows. It is applicable to cell-centred grids, both structured and unstructured, and includes a novel pressure stabilisation technique of the "momentum interpolation" type. Stabilisation of the velocity and stresses is achieved through a "both sides diffusion" technique and the CUBISTA convection scheme, respectively. A second-order accurate temporal discretisation scheme with adaptive time step is employed. The method is used to obtain benchmark results of lid-driven cavity flow, with the model parameters chosen so as to represent Carbopol. The results are compared against those obtained with the classic Herschel-Bulkley model. Simulations are performed for various lid velocities, with slip and no-slip boundary conditions, and with different initial conditions for stress. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted.